Effective Material Property Extraction of a Metamaterial by Taking Boundary Effects Into Account at Te/Tm Polarized Incidence

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In this paper, we present the extraction for efiective material parameters for a metamaterial from TE or TM waveguide measurements with generalized sheet transition conditions (GSTCs) used to provide electric and magnetic surface susceptibilities that approximate boundary efiects between the metamaterial and air. The retrieval algorithm determines the efiective material properties via scattering data obtained from the metamaterial in a waveguide. The efiective refractive index is expressed as a function of S-parameters for two samples of difierent length. The efiective wave impedance is given in terms of S-parameters and the refractive index, assuming that GSTCs account for the boundary efiects. The efiective permittivity and permeability can then be determined through the refractive index and wave impedance. By use of S-parameters generated by commercial three-dimensional (3-D) full-wave simulation software our present equations are tested for two cases of metamaterials: magneto-dielectric (r = r) and dielectric (TiO2) particles. We also conduct S-parameter measurements on dielectric cubes with an S-band (WR-284) waveguide to compute the efiective material properties. Furthermore, our results are compared to those derived from another retrieval method used in the literature, which does not account for boundary efiects.